The thesis is organized as follows. In the following chapter, we review relevant literature in the areas of robotic grasping, robotic assembly, and modular robotics. Part II presents our work on robotic grasping with modular robots. This part builds on our previous work presented in Seo et al. (2012), Seo and Kumar (2012), Seo et al. (2013b). Chapter 3 introduces concepts and terminology necessary to develop our theory and algorithms. Chapter 4 discusses three types of immobilizing grasps using curved effectors that can be applied to a wide range of objects including polyhedra. Chapter 5 discusses three types of cages derived from the immobilizing grasps and explains how to establish sufficient conditions for caging. Chapter 6 presents an algorithm for synthesizing the immobilizing grasps and cages. Chapter 7 extends our theory by adding more types of grasps and cages. Chapter 8 discusses
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the implementation of our approach on a modular robot system, with experiments. Part III is concerned with developing assembly planning algorithms for con- structing modular structures. This part builds on our previous work presented in Seo et al. (2013a), O’Hara et al. (2014). Chapter 9 describes our approach to design- ing the algorithms. Chapter 10 presents our first algorithm that supports parallel assembly and discusses its correctness. Chapter 11 presents our second algorithm, which can address target structures with internal holes, and discusses its correct- ness. Chapter 12 discusses the implementation of the algorithms, with experiments. Chapter 13 addresses how to extend the algorithms to more general patterns.
Chapter 2
Literature Review
This chapter outlines literature on robotic grasping, robotic assembly, and modular robotics that is relevant to this thesis.
2.1
Robotic Grasping
Robotic grasping has been an active research area over the past few decades. We here divide the prior work into two categories: one focusing on immobilizing objects by making contacts (prehensile approach) and the other based on caging (non-
prehensile approach). For each approach, we introduce theoretical aspects and
examples of robotic systems. See Bicchi and Kumar (2000) for a more general survey.
2.1.1
Prehensile Approach
We begin with discussing the closure properties of grasps. A grasp is defined as
force closed (Nguyen 1988) if and only if it can resist any external wrench. If a
grasp is force closed with frictionless contacts, it is said to be form closed (Lak-
shminarayana 1978) or immobilized (Rimon and Burdick 1998a). Trinkle (1992)
proposed a quantitative test formulated as a linear program for detecting form closure. Markenscoff et al. (1990) showed that it is possible to immobilize a three- dimensional object with seven frictionless point contacts, using first-order theories based on contact normals. Algorithms for synthesizing force or form closed grasps were presented by Ponce et al. (1997), Borst et al. (1999), Van der Stappen et al. (1999). Rimon and Burdick (1998a,b) developed a second-order mobility theory for rigid bodies in contact where the curvature properties at the contacts are taken
into account. Czyzowicz et al. (1991) showed that n+ 1 frictionless point contacts
suffice to immobilize a general n-dimensional polytope by using the effects of rela-
tive curvature; thus, for a three-dimensional object, four frictionless point contacts suffice for immobilization.
It has been discovered that the stability of a grasp depends on the geometry of the grasp, contact forces, and material properties. Mason and Salisbury (1985) established a framework for testing the stability of a grasp: a grasp is stable if its stiffness matrix is positive definite. Cutkosky and Kao (1989) showed that grasp stability is a function of local geometry, fingertip models, and the compliance of
the fingers. Nguyen (1989) proved that all force closed grasps can be made stable. Howard and Kumar (1996) established a framework for analyzing grasp stability that takes compliance, contact forces, and the local curvature properties of the bodies in contact into account. It was shown that immobilization implies dynamic stability with elastic contacts (Rimon and Burdick 1998a,b).
In practice, having a large number of contacts can be beneficial to grasp stabil- ity; however, synthesizing such a grasp can be computationally intractable. Pollard (2004) presented an efficient algorithm for synthesizing many-contact grasps based on user-provided examples. Similar approaches can also be seen in the literature on whole-body grasping (Hsiao and Lozano-Perez 2006) and enveloping grasping (Trin- kle et al. 1988). Napier (1956) showed that there are two approaches to achieving stability in human grasping: power grip and precision grip. Whole-body grasps and enveloping grasps are in the same vein of the human power grip, where an object is held by a large number of contacts between the flexed fingers and the palm.
Since Hanafusa et al. (1977) presented one of the earliest examples of robotic hands, various robotic hands have been developed. Our work is relevant with the approach to building simple yet versatile end-effectors that can be seen in Jacobsen et al. (1986), Ulrich et al. (1988), Dollar and Howe (2010), Kragten et al. (2011), Mason et al. (2012). Another relevant approach can also be seen in the literature on modular fixturing (Brost and Goldberg 1996, Ponce 1996). Recently, there has been growing interest in developing robotic systems that can grasp/manipulate ob-
jects with some autonomy. Saxena et al. (2008) presented a vision-based approach to robotic grasping and demonstrated real systems that can grasp previously un- known objects using two-dimensional images; similar approaches can be seen in Morales et al. (2002), Bowers and Lumia (2003). Hudson et al. (2012) developed an autonomy system that can perform dexterous, high-precision tasks such as key insertion.
2.1.2
Non-Prehensile Approach
In contrast to the prehensile approach, the literature on caging investigates how to arrange “obstacles” (that is, robotic fingers or effectors) around an object so as to bound its mobility without necessarily making contact. Caging allows us to sidestep some difficult issues such as modeling contacts or optimizing contact forces although the caged object may have some freedom to move. Rimon and Blake (1999) formulated a technique for computing cages of two-fingered hands; Davidson and Blake (1998a) extended the result to three-fingered hands. Vahedi and van der Stappen (2008a,b,c, 2009) provided an algorithm for synthesizing cages of two and three fingers around polygonal objects and formalized the concepts of squeezing and stretching cages for polygonal objects, which were generalized by Rodriguez and Mason (2009) to address objects in Euclidean spaces of arbitrary dimension. Allen et al. (2012) presented a simpler algorithm for computing two- fingered cages for polygons based on contact space analysis. Wan et al. (2012)
proposed a solution to synthesizing three-finger cages on the plane where two of the fingers are fixed. Other interesting approaches include Zamfirescu (1995), Maehara (2011), Fruchard (2012) where they investigated how to cage objects with just a single circle. Rodriguez et al. (2012) discussed the relationship between caging and grasping: they investigated when a cage can be a useful waypoint to an equilibrium grasp.
Recently, there have been efforts to take advantage of caging to robustify robotic tasks. Davidson and Blake (1998b) presented error-tolerant, vision-based planar grasping by closing fingers that form a cage. Gopalakrishnan and Goldberg (2002) presented a simple gripper with two vertical, parallel cylindrical jaws that can sta- bly grasp objects by forming a cage on concavities. Diankov et al. (2008) proposed a motion planning algorithm for performing manipulation tasks with cages, relax- ing task constraints. Yokoi et al. (2009) presented an approach to transporting objects using cages formed by not only robots but also the environment such as walls. Cappelleri et al. (2011a,b) employed cages formed by micro-manipulators for transporting and manipulating micro-scale polygonal parts. Dogar and Srini- vasa (2011) showed that simple manipulation such as quasi-static pushing can help robots stably cage and grasp objects even in clutter. There is a body of literature featuring decentralized approaches to caging; we refer the reader to Section 2.3.3.
2.2
Assembly Planning
Robotic assembly is a broad topic that is involved with a wide variety of issues in manipulating objects, which include grasping, caging, fixturing, pushing, and part orienting. See Mason (2001) for a general introduction. We here focus on the literature on assembly planning. According to Halperin et al. (2000), assembly planning is defined as the problem of finding and sequencing the motions that put the initially separated parts of an assembly together to form the assembled product. Lozano-Perez (1976) is one of the earliest works that focus on specific issues in planning mechanical assembly. The problem is generally approached by
considering how to establish a disassembly plan from a final product.
2.2.1
Assembly Sequencing
Assembly sequencing is a variant of assembly planning that received early atten- tion. In assembly sequencing, the parts of an assembly are often assumed to be free-flying, sidestepping issues such as how to physically perform assembly oper- ations and focusing on the geometric constraints imposed by the product itself. However, Assembly sequencing is a hard problem; Natarajan (1988), Kavraki and Kolountzakis (1995) discuss the PSPACE-hardness or NP-completeness of instances of assembly sequencing. De Fazio and Whitney (1987) presented a method for generating all valid assembly sequences based on a user input on the geometric relationships of the parts. Homem de Mello and Sanderson (1990) presented the
hypergraph representation of assembly plans that combines all feasible assembly sequences for a given product; the representation enables the selection of the best assembly plan and parallel execution of assembly operations. Ko and Lee (1987), Arkin et al. (1989), Wilson and Rit (1990) also presented similar approaches. Wil- son and Latombe (1994) presented the notion of a non-directional blocking graph, representing the geometric interferences among the parts in an assembly, which allows assembly sequences to be computed in polynomial time.
2.2.2
Beyond Traditional Assembly Sequencing
The traditional approach to assembly sequencing has been generalized in many directions. Latombe et al. (1997), Thomas et al. (2003), Ostrovsky-Berman and Joskowicz (2006) investigated assembly planning for toleranced parts. Halperin et al. (2000) presented a general framework for assembly planning that can address additional constraints such as toleranced parts, stability, and tool use. Romney (1997) presented a method to concurrently generate an assembly sequence and de- sign a fixture to hold intermediate subassemblies. Mosemann et al. (1998), Rakshit and Akella (2014) presented assembly/disassembly sequencing that takes part sta- bility into account in the presence of external forces such as gravity and friction.
Assembly planning can also be understood as a variant of robot motion planning where the goal is to assemble robotic parts into one coherent structure (LaValle 2006). Sundaram et al. (2001) presented an approach for disassembly sequencing
based on sampling-based robot motion planning. Similar approaches can also be seen in Ferre and Laumond (2004), Le et al. (2009).